Direct input of monitoring data into a mechanistic ecological model as a way to identify the phytoplankton growth-rate response to temperature variations

We present an approach (knowledge-and-data-driven, KDD, modeling) that allows us to get closer to understanding the processes that affect the dynamics of plankton communities. This approach, based on the use of time series obtained as a result of ecosystem monitoring, combines the key features of both the knowledge-driven modeling (mechanistic models) and data-driven (DD) modeling. Using a KDD model, we reveal the phytoplankton growth-rate fluctuations in the ecosystem of the Naroch Lakes and determine the degree of phase synchronization between fluctuations in the phytoplankton growth rate and temperature variations. More specifically, we estimate a numerical value of the phase locking index (PLI), which allows us to assess how temperature fluctuations affect the dynamics of phytoplankton growth rates. Since, within the framework of KDD modeling, we directly include the time series obtained as a result of field measurements in the model equations, the dynamics of the phytoplankton growth rate obtained from the KDD model reflect the behavior of the lake ecosystem as a whole, and PLI can be considered as a holistic parameter.

The system of the Naroch Lakes is located in the northwestern Belarus in the Neman River basin and includes three water bodies: Lake Batorino, Lake Myastro, and Lake Naroch. These water bodies are interconnected by channels. The main characteristics of the Naroch Lakes are given in Table 1. The Naroch Lakes are completely frozen for much of the period from the late November to April.

Field sampling
Water samples were collected monthly at specific monitoring points at the pelagic zones of the lakes during the vegetative season (from May to October) with the use of the two-liter Ruttner sampler. The samples were collected from six different depths (0.5, 3, 6, 8, 12 and 16 m) in Lake Naroch(54°53'10.56"N, 26°43'12.12"E), four depths (0.5, 4, 7 and 9 m) in Lake Myastro (54°52'0.91"N, 26°52'49.86"E), and three depths (0.5, 3 and 5 m) in Lake Batorino (54°50'47.94"N, 26°58'3.36"E). The water samples from all the depths were mixed in such a way that the water volume of each level (depth) in the mixed sample was proportional to the fraction of the level in the total water volume in each of the lakes according to bathymetry. At the same depths, water temperature was measured using a mercury deep-water thermometer with a scale resolution of 0.1°C.

Phyto-and zooplankton
Samples of 0.5 liters for phytoplankton and 10 liters for zooplankton measurements were taken out from each of the mixed samples. Phytoplankton samples were fixed with Utermöhl's solution [1]. Then the samples were sedimented in total darkness for not less than one week. These samples were concentrated very accurately up to 100-150 ml by pouring off all excess water with the use of thin silicon or rubber siphon covered with two-layer silk sieve with 77 μm mesh. The resulting concentrate was poured into plankton bottles and settled for no less than 2 -3 days. Then the extra water was drawn off using a medical syringe with thin vinyl tubule at its end. Finally, the actual sample volume was 15 -30 ml depending on the sediment thickness. The light Zeiss Axiolab microscope was used to analyze phytoplankton samples. The phytoplankton abundance is expressed in cell number (number of one-celled species, number of cells in filaments and colonies) per liter. A Fuchs-Rosenthal chamber with a volume of 3.2 mm 3 was used to count small phytoplankton individuals. The larger phytoplankton such as Ceratium, Asterionella, Melosira, Aulacoseira, Tabellaria, Fragilaria, Microcystis, Coelosphaerium, Anabaena, and some others were counted with the use of a 1 ml chamber while large colonial organisms (Gloeotrichia echinulata, Volvox) were counted with the use of a Bogorov chamber Estimation of phytoplankton biomass was carried out by "the Kiselev's method of true volumes" [2]. Using this method, cell or organism volumes were calculated for each species by applying a solid geometric shape (ellipsoid, sphere, rod, cone, etc.) most closely matching with the shape of the cells or organisms [3,4]. The relative density of phytoplankton was set to 1. The total biomass of phytoplankton was calculated by taking the sum of the biomass of each isolated individual.
The zooplankton samples were filtered using Apstein plankton net with 64 μm mesh size.
Resulting sediment with a volume of 150 ml was poured into a plastic bottle filled with 4% formalin and it settled for 10 days. Then, the sample volume was reduced to 50 ml by decanting of top layer without stirring-up of sediment. The silicon siphon covered with 55 μm mesh net was used for the decanting. With a pipette dispenser, 2 -6 ml of the sample was taken off for analysis. Counting and zooplankton species identification were carried out with two repetitions using microscopes Below we present the results of field measurements, which were carried out in 2006 -2018 in the Naroch Lakes.